Candidates fanned out across the country Wednesday, picking and choosing their battles among the dozens of upcoming primary states as the presidential race finally expanded beyond the tunnel vision of Iowa and New Hampshire.

With different sets of winners in the presumably crucial early test states, the race is even more unsettled than it was on the eve of the Jan. 3 Iowa caucuses.

The Republican race is a game of Chinese checkers, where candidates keep leap-frogging over one another in hopes of reaching the end of the line.

One-time national front-runner Rudy Giuliani has been trumped in the national polls by John McCain, who won New Hampshire, and Mike Huckabee, who won Iowa. Former Massachusetts Gov. Mitt Romney is hoping his two second-place finishes will build toward victory in Michigan, where his father was governor, and former Tennessee Sen. Fred Thompson is eyeing the first-in-the-South primary in South Carolina as his time to shine.

Off to South Carolina: Tune in Thursday at 9 p.m. ET as the South Carolina Republican Party and FOX News host the Republican candidates debate live from Myrtle Beach.

The Democratic race is 1-1. Barack Obama's consuming momentum after his Iowa win was tempered Tuesday by Hillary Clinton's strong and surprising showing in New Hampshire, which she took by 3 points. John Edwards, who placed second in Iowa and third in New Hampshire, promised to soldier on.

Click here to see photos from the campaign trail.

The rest of January will be a scramble, as Michigan, Nevada, South Carolina and Florida all play prelude to the Feb. 5 "Super Tuesday" battle for nearly two-dozen primary states. Michigan is mostly an afterthought for Democrats, though, since the state lost its Democratic convention delegates as punishment for scheduling an early primary. Attention now is geared toward Nevada and South Carolina first.

Clinton and Obama immediately wiped the slate clean and started talking about the remaining 48 states Wednesday.

"It was an emotional roller ride," Clinton told FOX News Wednesday, saying she already began to feel a shift. "I feel very good about the judgment the people of New Hampshire made yesterday. And you know, today I'm up and I'm at it, and I'm going to keep going as we take on all the rest of the contests between now and February 5th."

Clinton's campaign released a detailed memo Wednesday outlining its tactics in more than a dozen states: compiling phone banks in South Carolina, announcing endorsements in Nevada, holding ‘Honk and Holler for Hillary' rallies in California and a long list of other items.

Chairman Terry McAuliffe said in a conference call Wednesday morning that the campaign received close to $750,000 in contributions online since Clinton's victory speech. On reports that Bill Clinton-era advisers would soon be joining the campaign, he said only that the campaign always planned to make room for more advisers as they shift gears toward Feb. 5.

Obama's campaign didn't miss a beat either, releasing a memo claiming it raised $8 million in the first eight days of 2008 and saying the campaign is well-positioned financially to compete in the primaries ahead. The campaign also reported raising $500,000 in online contributions since Tuesday night.

The memo said the campaign would have deep organizations in Nevada and South Carolina, and that it has staff in 19 of 22 Feb. 5 states. The campaign plans to staff up the remaining Delaware, Arkansas and Connecticut offices by the end of the week, and claims it already has active chapters at the bulk of the colleges and universities in the Feb. 5 states.

Democrats are carefully eyeing the Nevada caucuses Jan. 19 where Hispanic voters will have a heavier voice, and Clinton and Obama are locking horns over the strong union vote that pervades Las Vegas. Obama quickly landed a post-New Hampshire blow by securing the endorsements of the state chapter of the Service Employees International Union and Nevada's largest labor group, the Culinary Workers Union. Clinton's union support lies in more established groups like the American Federation of State, County and Municipal Employees.

"You know, we've got a great base, a great organization down in South Carolina," Obama told FOX News. "And what we've seen is just as happened in New Hampshire, the polls closed and it's now very close in South Carolina. And I think that if we do well in Nevada, we come into South Carolina with a good head of steam, we feel confident that that's a state where we can do well."

Poll averages on RealClearPolitics.com Wednesday showed Clinton with a slight lead nationally, though it has shrunk from the 20-point buffer she once enjoyed. The averages show her with 37 percent, Obama with 30 percent and Edwards with nearly 18 percent.

Among the GOP candidates, Romney said the uneven results from the early test states mean it's time to scrap old strategies.

"Only a few months ago, as you know, the whole thought was, okay we gotta win Iowa, New Hampshire to get the momentum necessary to go up against this great powerhouse, the inevitable candidate, Rudy Giuliani -- and somehow Rudy Giuliani's inevitability is not inevitable anymore," Romney said Wednesday in Boston, where he raised $5 million during his National Call Day 2008 fundraiser. "And so there's no discussion about, you gotta be strong in the first two states to beat Rudy. That's not the issue anymore."

He said repeatedly he's going to win Michigan, which votes Jan. 15, even though he was making similar predictions before the New Hampshire's primary. Romney won the Wyoming GOP caucuses Saturday.

Looking forward, Romney's staffers say he's not abandoning South Carolina -- he's just pushing back scheduled events there until after Michigan, as aides say they're looking to boost chances in South Carolina following a win in Michigan. Romney has also decided to pull his advertising from South Carolina and Florida, where Giuliani has been spending time and money, in hopes of devoting airtime to Michigan.

Michigan is symbolically important to Romney. His father George Romney was a governor there who ran for president and later served in the Nixon administration, and the Romney name is well-established in state politics.

McCain campaigned in Michigan Wednesday as well, hoping to reprise his win there in 2000 just as he did in New Hampshire. There he did what he's been doing, stressing that he's the candidate best equipped to handle matters of national security.

"I can throw a dart at a map of the world and show you a place where there's national security challenges," McCain said before a Grand Rapids rally. "I'm the only one that's been involved in these issues for the last 20 years."

The Palmetto State primary, on Jan. 19 along with Nevada's, poses a different landscape for Republicans that could favor some candidates over others.

The GOP campaigns are modeling on the vote being between 50 and 60 percent evangelical, a bloc that boosted Huckabee, a Southern Baptist pastor, in Iowa.

But the state also has the nation's largest population per capita of active and retired military, which could bode well for McCain, a Vietnam veteran.

Direct mail attacks are expected to begin in the state today and peak over the weekend.

Thompson also set South Carolina as his firewall for a campaign that has yet to take off.

"I'm proud to say I am drawing a line in the sand in South Carolina," Thompson said Wednesday in Sumter. He bypassed New Hampshire's GOP campaign and finished last there.

He said he won't change his style for political expediency. "What you see is what you get," he said. "If they like that, I'll be in great shape."

RealClearPolitics.com averages showed Huckabee still leading slightly on the national level. The averages gave Huckabee 21.3 percent, McCain 20 percent, Giuliani 16.3 percent, Romney 13.3 percent, Thompson 11 percent and Texas Rep. Ron Paul 3.7 percent.

Huckabee too arrived in South Carolina Wednesday predicting a win and hoping to consolidate support to prove his appeal goes beyond Iowa.

"We want to do more than do well here," Huckabee said. "I want to make it real clear. We're going to win South Carolina."

He also came out with an ad in Michigan that's a not-so-subtle swipe at Romney.

The ad, called "Understanding," bemoans the loss of manufacturing jobs and the rise of fuel costs. He highlights cutting taxes and building highways as Arkansas governor, but at the end of the spot says "I believe most Americans want their next president to remind them of the guy they work with, not the guy who laid them off" -- a line he's used to jab at venture capitalist Romney.

Click here to see the Huckabee ad.

South Carolina could also prove decisive for Edwards, who made a point that there's 48 states left to go after the polls closed in New Hampshire Tuesday night.

Edwards -- who was born in South Carolina and later became a North Carolina senator -- has a southern lilt and a populist message, and his lagging numbers from the contests so far indicate that he needs a win. He's hoping to reprise his win in the state from the 2004 primary.

Democrats go head-to-head in South Carolina on Jan. 26 a week after Republicans, and Edwards returned there for a "homecoming rally" at Clemson University Wednesday. The campaign said more than 1,000 South Carolina supporters greeted him.

FOX News' Carl Cameron, Aaron Bruns and Shushannah Walshe and The Associated Press contributed to this report.